• Deciding EA-equivalence via invariants 

      Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2022)
      We define a family of efficiently computable invariants for (n,m)-functions under EA-equivalence, and observe that, unlike the known invariants such as the differential spectrum, algebraic degree, and extended Walsh spectrum, ...
    • A direct construction of even length ZCPs with large ZCZ ratio 

      Kumar, Praveen; Sarkar, Palash; Majhi, Sudhan; Paul, Subhabrata (Journal article; Peer reviewed, 2022)
      This paper presents a direct construction of aperiodic q-ary (q is a positive even integer) even length Z-complementary pairs (ZCPs) with large zero-correlation zone (ZCZ) width using generalised Boolean functions (GBFs). ...
    • Encoding and decoding of several optimal rank metric codes 

      Kadir, Wrya Karim Kadir; Li, Chunlei; Zullo, Ferdinando (Journal article; Peer reviewed, 2022)
      This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation ...
    • An infinite family of 0-APN monomials with two parameters 

      Kaleyski, Nikolay Stoyanov; Nesheim, Kjetil Amundsen; Stănică, Pantelimon (Journal article; Peer reviewed, 2023)
      We consider an infinite family of exponents e(l, k) with two parameters, l and k, and derive sufficient conditions for e(l, k) to be 0-APN over F2n . These conditions allow us to generate, for each choice of l and k, an ...
    • Invariants for EA- and CCZ-equivalence of APN and AB functions 

      Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2021)
      An (n,m)-function is a mapping from \({\mathbb {F}_{2}^{n}}\) to \({\mathbb {F}_{2}^{m}}\). Such functions have numerous applications across mathematics and computer science, and in particular are used as building blocks ...
    • Modeling and simulating the sample complexity of solving LWE using BKW-style algorithms 

      Guo, Qian; Mårtensson, Erik Axel Fredrik; Stankovski Wagner, Paul (Journal article; Peer reviewed, 2022)
      The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, ...
    • A number theoretic view on binary shift registers 

      Petrides, George (Journal article; Peer reviewed, 2022)
      We describe a number theoretic view on binary shift registers. We illustrate this approach on some basic shift registers by revisiting known and obtaining new results, which we prove using tools from basic number theory, ...
    • On decoding additive generalized twisted Gabidulin codes 

      Kadir, Wrya; Li, Chunlei (Journal article; Peer reviewed, 2020)
      In this paper, we consider an interpolation-based decoding algorithm for a large family of maximum rank distance codes, known as the additive generalized twisted Gabidulin codes, over the finite field Fqn for any prime ...
    • On relations between CCZ- and EA-equivalences 

      Villa, Irene; Calderini, Marco; Budaghyan, Lilya (Peer reviewed; Journal article, 2020)
      In the present paper we introduce some sufficient conditions and a procedure for checking whether, for a given function, CCZ-equivalence is more general than EA-equivalence together with taking inverses of permutations. ...
    • On the behavior of some APN permutations under swapping points 

      Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Riera, Constanza Susana; Stanica, Pantelimon (Journal article; Peer reviewed, 2022)
      We define the pAPN-spectrum (which is a measure of how close a function is to being APN) of an (n, n)-function F and investigate how its size changes when two of the outputs of a given function F are swapped. We completely ...
    • On the Boomerang Uniformity of some Permutation Polynomials 

      Calderini, Marco; Villa, Irene (Journal article; Peer reviewed, 2020)
      The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials, one for the upper ...
    • On the EA-classes of known APN functions in small dimensions 

      Calderini, Marco (Journal article; Peer reviewed, 2020)
      Recently Budaghyan et al. (Cryptogr. Commun. 12, 85–100, 2020) introduced a procedure for investigating if CCZ-equivalence can be more general than EA-equivalence together with inverse transformation (when applicable). In ...
    • Triplicate functions 

      Budaghyan, Lilya; Ivkovic, Ivana; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2022)
      We define the class of triplicate functions as a generalization of 3-to-1 functions over \(\mathbb {F}_{2^{n}}\) for even values of n. We investigate the properties and behavior of triplicate functions, and of 3-to-1 among ...